Novel exponential-weighted integral inequality for exponential stability analysis of time-varying delay systems

Abstract

This paper investigates the exponential stability of systems with time-varying delays. A novel exponential-weighted integral inequality is developed from the extension of the second-order Bessel–Legendre inequality by introducing suitable coefficients into orthogonal polynomials, which leverages the monotonic property of certain integral ratios derived from orthogonal polynomials. This inequality enables the direct estimation of exponential-weighted integrals with varying limits, without requiring the additional conservative bounding commonly used in existing literature. Utilizing the proposed inequality, two exponential stability criteria are derived, corresponding to two different cases of time-varying delays. Simulations based on two well-studied examples demonstrate the effectiveness of the proposed approach.